We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total customer demand is random and comprises fixed proportion of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering among products. A customer purchases the highest-ranked product, according to his type (if any), that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help to characterize multiple local maxima. We use the properties of the optima to solve the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the mean demand is large, the degree of substitutability is high, the population is homogeneous, or prices and/or costs vary across products.

Assortment Planning and Inventory Decisions Under Stockout-Based Substitution

Retail store operations: Literature review and research directions

The share of gross domestic product from the service industry reflects the competitiveness of a nation; the service industry in the USA accounts for around 80% of its gross domestic product, and it has been increasing gradually. Continual innovations and advances in enabling technologies for the service industry are crucial for developed countries to sustain their leading positions in the globalized economy. To clarify future research directions of operations research (OR) in the service industry, the state of art of OR has been examined systematically, the new requirements of OR are identified for its applications in service industries in comparison with those in manufacturing industries, and the limitations of existing methodologies and tools have been discussed. This paper was intended to provide an updated review on how OR has been applied in the service sector in recent years and what directions the study of OR will be carried forward in the near future. Under a proposed research framework, recent OR-related articles were collected from 17 leading OR journals and classified into the five most active sectors, that is, transportation and warehousing, information and communication, human health and social assistance, retails and wholesales, and financial and insurance services. The conclusions on the limitations of existing studies and the demanding ORs in the service have been drawn from our summaries and observations from a comprehensive review in this field. Copyright © 2013 John Wiley & Sons, Ltd.

Operations Research (OR) in Service Industries: A Comprehensive Review

Pricing decisions for substitutable products in a two-echelon supply chain with firms' different channel powers

Product substitution in different weights and brands considering customer segmentation and panic buying behavior

In this paper, we examine the nature of optimal inventory policies in a system where a retailer manages substitutable products. We first consider a system with two products 1 and 2 whose total demand is D and individual demands are negatively correlated. A fixed proportion of the unsatisfied customers for an item will purchase the other item, if it is available in inventory. For the single period case, we show that the optimal inventory levels of the two items can be computed easily and follow what we refer to as "partially decoupled" policies, i.e. base stock policies that are not state dependent, in certain critical regions of interest both when D is known and random. Furthermore, we show that such a partially decoupled base-stock policy is optimal even in a multi-period version of the problem for known D for a wide range of parameter values and in an N-product single-period model under some restrictive conditions. Using a numerical study, we show that heuristics based on the de-coupled inventory policy perform well in conditions more general than the ones assumed to obtain the analytical results. The analytical and numerical results suggest that the approach presented here is most valuable in retail settings for product categories where the level of substitution between items in a category is not high, demand variation at the aggregate level is not high and service levels or newsvendor ratios are high.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1385016_code640676.pdf?abstractid=1140309&mirid=5

Inventory Models for Substitutable Products: Optimal Policies and Heuristics

This paper explores when it is important for firms to consider stockout-based substitution and competitor's inventory levels in making inventory decisions in the context of a duopoly model. To address this question, we consider a model where two newsvendors sell substitutable products in a market with aggregate market demand D. The two firms get a proportion p and (1-p) of this demand, where p is random. We characterize the equilibrium inventory levels of the two firms in a single-period model and show the striking property that under certain reasonable conditions on the cost parameters, the two firms ignore their competitor's inventory levels and potential substitution demand, i.e. their inventory decisions are decoupled. Furthermore, we show under slightly more restrictive conditions on the cost parameters that the single-period results can be extended to the case where D is random. Finally, we extend the "decoupling" property to a multi-period periodic review scenario and show that the resulting Nash equilibrium can be characterized simply as the solution to a single-product dynamic newsvendor problem that ignores substitution demand.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1385082_code640676.pdf?abstractid=1140311&mirid=1

Raj S. Rajagopalan

Papers

Inventory Models for Substitutable Products: Optimal Policies and Heuristics

A Multi-Period Model of Inventory Competition